more confusion on cessna performance chart

A little while ago I started a thread about why a Cessna landing
peformance chart showed a climb wt limit that was pressure altitude
rather than density altitude dependant. Well now I am similarly
confused by a different performance table ( not a chart this time)
which shows the take off distance required for a C172N. This table
shows the distance required as a function of pressure altitude form 0
to 8000 ft ( in steps of 1000 ft) and temperature of 0 to 40 deg C in
steps of 10 deg C. This table comes from the flight manual of the
aircraft.

Now I thought it would be a useful addition to my Excel flight fomulas
to convert all this data into a graph of distance required vs density
altitude and fit an equation to it, so then I could just enter density
altitude and the program would calculate distance required ( with
corrections for wind etc)
Well the problem is that where the density altitude ranges overlap for
the different temperatures the distance required differs with the
lower the temp, the higher the distance required for the same density
altitude.

At around 8000 ft density altitude the difference was like 300 ft
between 0 and 40 deg C which is quite significant. I am pretty sure I
know how to calculate density altitude, but just in case here is how I
do it,

Take the pressure altitude and correct for temperature as follows.
eg for 3000 ft pressure altitude and 30 deg C. ISA temp would be
(15-3x2)=+9 C, so we are 21 C over ISA temp. 21*120 =2520 +3000
=5520 ft density altitude

So why would the takeoff distance required vary with temperature at
the same density altitude?, it goes against everything I understood
about peformance being a function of the air density.

Any help appreciated.
Terry
PPL downunder

Rolling resistance of tires?

Hard to say what Cessna's assumptions are, especially when they didn't
include their formula, just a data set.

On Jan 15, 9:02*am, TakeFlight wrote:
Rolling resistance of tires?

Hard to say what Cessna's assumptions are, especially when they didn't
include their formula, just a data set.

I would think rolling resistance would be less at lower temperatures.
rubber softens at higher temps and gets a better grip. the data shows
the reverse , at lower temps for the same density altitude the
distance required is higher.

terry wrote:
On Jan 15, 9:02 am, TakeFlight wrote:
Rolling resistance of tires?

Hard to say what Cessna's assumptions are, especially when they didn't
include their formula, just a data set.

I would think rolling resistance would be less at lower temperatures.
rubber softens at higher temps and gets a better grip. the data shows
the reverse , at lower temps for the same density altitude the
distance required is higher.

Stiff tire sidewalls are harder to flex and thus absorb more energy in
the process. This is why radial tires, even though they flex more, have
lower rolling resistance than bias ply tires. It isn't intuitive, but
it is reality.

Matt

There is a very excellent text with derived equations for almost anything
having to do with flight. "The Axioms Of Flight" by James Embree, ISBN
0-9601062-7-8. I have most of the equations plugged into either Excel or
Basic and mostly they agree with "manufacturer's data" within an rch.

Jim

On Jan 16, 4:18*am, "RST Engineering" wrote:
There is a very excellent text with derived equations for almost anything
having to do with flight. *"The Axioms Of Flight" by James Embree, ISBN
0-9601062-7-8. *I have most of the equations plugged into either Excel or
Basic and mostly they agree with "manufacturer's data" within an rch.

Jim

Thanks for the reference. BTW what is an rch?
Terry

It is a steeped-in-tradition engineering convention used to describe
something that is very, very close to the correct answer. It derives from
the very fine hair found on the lower-midsection of the adult female, of
which the red has been experimentally found to be the smallest in diameter.

It took centuries of trial and measurement to prove this experiment correct
{;-)


Jim
--
"If you think you can, or think you can't, you're right."
--Henry Ford




Thanks for the reference. BTW what is an rch?
Terry

roflol, what kinds of experiments are/were needed to prove
the axiom?



"RST Engineering" wrote in message
...
| It is a steeped-in-tradition engineering convention used
to describe
| something that is very, very close to the correct answer.
It derives from
| the very fine hair found on the lower-midsection of the
adult female, of
| which the red has been experimentally found to be the
smallest in diameter.
|
| It took centuries of trial and measurement to prove this
experiment correct
| {;-)
|
|
| Jim
| --
| "If you think you can, or think you can't, you're right."
| --Henry Ford
|
|
|
|
| Thanks for the reference. BTW what is an rch?
| Terry
|
|

On Jan 16, 4:44*am, "RST Engineering" wrote:
It is a steeped-in-tradition engineering convention used to describe
something that is very, very close to the correct answer. *It derives from
the very fine hair found on the lower-midsection of the adult female, of
which the red has been experimentally found to be the smallest in diameter..

It took centuries of trial and measurement to prove this experiment correct
{;-)

Well thanks for that Jim. Downunder we have a similar but slightly less technical saying for something that is very close. It is called "within a bees dick"

Terry

On Mon, 14 Jan 2008 12:56:46 -0800 (PST), terry wrote:

So why would the takeoff distance required vary with temperature at
the same density altitude?

I confess that I'm lazy today and didn't read what you said for
comprehension, but I will address the above statement.

DA mantra:
Density altitude is pressure altitude corrected for non-standard
temperature.

Ok, so if DA has been corrected for temperature, then we're done.

The "vary with temperature" part of your statement doesn't make any sense
if you are using DA, the temperature factor has been applied already. You
wouldn't apply temperature again to come up with an answer.

The statement above would make sense if you said: The takeoff distance
required will vary with temperature at the same "pressure altitude".


--
Dallas